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This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/LRA.2019.2899189, IEEE Roboticsand Automation Letters

IEEE ROBOTICS AND AUTOMATION LETTERS. PREPRINT VERSION. ACCEPTED JANUARY, 2019 1

Abstract—Magnetic resonance imaging (MRI)-guided

intervention has drawn increasing attention over the last decade.

It is accredited to the capability of monitoring any physiological

change of soft tissue with the high-contrast MR images. This also

gives rise to the demand for precise tele-manipulation of

interventional instruments. However, there is still lack of choices

of MR safe actuators that provide high-fidelity robot

manipulation. In this paper, we present a three-cylinder hydraulic

motor using rolling-diaphragm-sealed cylinders, which can

provide continuous bidirectional rotation with unlimited range.

Both kinematics and dynamics models of the presented motor

were studied, which facilitate its overall design optimization and

position/torque control. Motor performance, such as step

response, frequency response, and accuracy, were experimentally

evaluated. We also integrate the motor into our catheter robot

prototype designed for intra-operative MRI-guided cardiac

electrophysiology (EP), which can provide full-degree-of-freedom

and precise manipulation of a standard EP catheter.

Index Terms— Hydraulic actuators, medical robotics, MR safe

robot, catheterization, robot-assisted intervention

I. INTRODUCTION

AGNETIC resonance imaging (MRI) is well-known for

its superior capabilities in providing non-invasive,

non-ionizing radiation high-contrast images of soft tissues, and

also in monitoring the temperature changes during thermal

therapy procedures [1]. These advantages prompted the

adoption of MRI guidance for interventions ranging from

biopsy [2], thermal therapy for tumor ablation [3], drug

delivery [4] to catheter-based procedures within cardiovascular

system [5, 6]. However, precisely manipulating the instrument

within the limited workspace of MRI bore still remains

challenging. A number of research attempts [7, 8] have focused

on developing tele-operated robotic platforms for the

Manuscript received: September 10, 2018; Revised: December 17, 2018;

Accepted January 24, 2019. This paper was recommended for publication by Editor Paolo Rocco upon evaluation of the Associate Editor and Reviewers’ comments. This work is supported in parts by Signate Life Sciences (Hong Kong) Limited, the Croucher Foundation, the Research Grants Council (RGC) of Hong Kong (Ref. No. 27209151, No. 17227616, and No. 17202317).

Z. Dong, Z. Guo, K.H. Lee, G. Fang, W. L. Tang and K.W. Kwok are with Department of Mechanical Engineering, The University of Hong Kong, Hong Kong (corresponding author, Tel: +852-3917-2636; e-mail: [email protected]).

H.C. Chang is with Department of Diagnostic Radiology, The University of Hong Kong, Hong Kong.

D.T.M. Chan is with Department of Surgery, The Chinese University of Hong Kong, Hong Kong.

Digital Object Identifier (DOI): see top of this page.

interventions, demonstrating enhanced accuracy and reduced

procedural time under intra-operative (intra-op) MRI.

The early MRI-guided robot was developed by Chinzei et al.

[9] in brachytherapy of prostate cancer. The robot is actuated by

piezoelectric motors, which make use of high-frequency

current to excite precise stepping action. In order to minimize

the EM interference, the motors have to be placed far away

from the imaging region to manipulate the interventional tools.

Recent studies (Su et al. [10]) also explore the use of

tailor-made components to attenuate the EM interference.

Much effort has also been made in designing the EM-shield

enclosures, and also customizing the motor driver for low loss

of SNR (2%) during their motor operation. Nevertheless, due to

the fundamental working principle of stepping and friction

driven, it is challenging to apply piezoelectric motor to

procedures which require outstanding dynamic performance.

Inherently MR safe motors powered by fluid, e.g. pneumatic

motors [11-13], have also been widely discussed. Stoivanici et

al. [14] developed a robot for intra-op MRI-guided prostate

biopsy, which was fully driven by pneumatic stepper motors.

Groenhuis et al. [15] did various prototypes for breast biopsy.

Their motor design is compact and seamlessly integrated with

the robot for precise manipulation of a needle. However, other

than biopsy, particularly in certain procedures demanding for

prompt and responsive manipulation/navigation of instruments,

e.g. electrophysiology (EP) catheterization in dynamic

cardiovasculatures, the high compressibility of air will cause

difficulties in handling the dynamics and also the mechanical

transmission delay. Moreover, delicate handling of regulation

valves and air dissipation is needed to avoid excessive noise

High-performance Continuous Hydraulic Motor

for MR Safe Robotic Teleoperation

Ziyang Dong, Ziyan Guo, Kit-Hang Lee, Ge Fang, Wai Lun Tang, Hing-Chiu Chang, Danny Tat Ming Chan and Ka-Wai Kwok, Senior Member, IEEE

M

Fig. 1. Setup of the three-cylinder motor in the 1.5T MRI scanner. This MR safe motor is connected with three pipelines which transmit motion from the master unit in the control room. The MR image of an MRI phantom placed aside the actuator indicates the negligible EM interference.




and vibration, along with the acoustic noise existing from MRI

scanner (~100dB), which may cause patient anxiety.

Therefore, hydraulic actuation using incompressible fluid

(e.g. water, oil) as transmission media can offer much faster

response and higher power density [16, 17]. However,

conventional piston-cylinder paradigm often suffers from large

Coulomb friction due to the tight O-ring sealing, which

introduces substantial mechanical losses and nonlinearities to

the control system. Whitney et al. [18] developed an efficient

fluid transmission based on the rolling-diaphragm-sealed

metallic cylinders, which can greatly reduce the mechanical

friction. This concept has been adopted to our recent

MRI-guided robotic catheterization platform [19] that is made

of solely non-metallic materials. The system has demonstrated

accurate and dexterous manipulation of EP catheter. However,

the diaphragm can only be flipped inside out with a limited

stroke (Fig. 2a), which is insufficient to navigate the full length

required in EP. Although the effective stroke can be increased

by gearing up the actuator, it will inevitably compromise the

output torque and durability of non-metallic components.

This poses strong incentive to develop a novel integration

method of these fluid transmissions, which is MR safe and

capable of bi-directional rotation with infinite range and high

payload. Such technique is expected to resolve many

bottlenecks involved in teleoperating MRI-guided surgical

apparatus. For example, high-intensity focused ultrasound

(HIFU) thermal therapy under MRI is a noninvasive ablation

approach, which currently still relies on manual positioning of a

heavy ultrasound transducer array.

In this paper, with the aim to solve the unmet clinical needs

for tele-operated, dexterous control of interventional tools

under MRI, we propose an MR safe motor design capable of

providing unlimited range of continuous bidirectional rotation

(Fig. 1). These capabilities would be comparable to the

conventional EM-motor for versatile applications even

involving high payload manipulation. The key contributions of

our work are listed below:

1) Design of a three-cylinder hydraulic motor for

high-performance tele-operation of MRI-guided robotic

interventions. It can achieve continuous bidirectional actuation

with unlimited motion range. The motor can also be customized

with more cylinders (>2) to provide higher output torque;

2) Dynamics modelling of the hydraulic actuation was

studied for design optimization. Both positional and torque

control can be applied;

3) Experimental validation of transmission step response,

force transmission, frequency response and accuracy are

conducted to ensure dexterous robotic actuation. The

three-cylinder hydraulic motor has also been integrated into an

MR safe robotic platform for cardiac catheterization, which is

tested by a long-range navigation task.

II. DESIGN OF DIAPHRAGM-BASED HYDRAULIC

TRANSMISSION

Fig. 2a shows a pair of cylinders enabling

action-and-reaction transmission via a long hydraulic tube

(10-meter) that passes through the waveguide in between MRI

and control room. Incompressible liquid, such as water or oil, is

fully filled in the pipelines to ensure responsive, accurate power

transmission in both directions. Considering the trade-off

between pliability and stiffness of the tube for such

long-distance transmission, semi-rigid nylon tubes with

outer/inner diameter of Ø6/4 mm (DG-5431101, Daoguan Inc.)

are selected. Radial expansion of these tubes under loading is

minimal when the transmission liquid inside is pressurized.

Key components in our current prototype, such as piston rods

and cylindrical housings, are 3D-printed with polymer

composites (VeroWhitePlus and VeroClear, Stratasys, US),

ensuring the MR safety. To enhance the structural rigidity and

robustness in production stage, alternative choices of MR safe

materials with higher strength, e.g. polyethylenimine,

polyoxymethylene, will be explored and adopted.

Each cylinder unit contains a rolling diaphragm

(MCS2018M, FEFA Inc.) made of fabric-reinforced rubber for

fluid sealing. The diaphragm can be flipped inside out, and roll

Fig. 2. (a) Pair of cylinders enabling MR safe power transmission through a long hydraulic tube via the waveguide in-between control room (master control side) and MRI suite (slave robot side). Rolling diaphragms are adopted to tightly sealed the fluid, and also to slide inside the cylinder with minimal friction. (b) 3D model showing the piston rods coupled with the output shaft by hinging a rotating plate and crankshaft; (c) Kinematics parameters denoted in a single cylinder, which are summarized in (d).



DONG et al: HIGH-PERFORMANCE MR SAFE CONTINUOUS HYDRAULIC MOTOR 3

over the piston rod to allow 35-mm stroke linear motion. Its

working principle inherently averts the sliding friction between

the seal and cylinder, which is a great concern in the

conventional O-ring-sealed hydraulic transmission [18].

However, the transmission can only take place when the piston

rod is pushed onto the diaphragm hat. Therefore, only

one-to-one cylinders cannot conduct bidirectional

transmission. In this light, the integration of multiple cylinders

pairs is proposed to generate actuation in both directions. Our

previous work demonstrated the two-cylinder configuration

[19]. However, the short motion range is still far from

satisfying requirements for high-precision and long-range

navigation, e.g. for needle insertion (>100 mm [20]) or EP

catheterization from femoral vein to heart chamber. To this end,

fundamental change of cylinders configuration is proposed to

resolve the unmet technical/clinical requirements.

A. Continuous actuation with three-cylinder configuration

Fig. 1 and Fig. 2b show the prototype and 3D model of the

proposed MR safe motor, respectively. It integrates three

hydraulic cylinders. This design is capable of bidirectional,

continuous and torque-controllable rotatory actuation, in

contrast to aforementioned stepper motors with pneumatic

cylinders that only allow full-stroke movement [21].

Continuous motion is made possible by taking advantage of the

rolling diaphragm seal, which enables precise control of

displacement/force of each cylinder, even when connected

through 10-meter hydraulic pipelines.

The output shaft of our motor is simultaneously driven by all

cylinders, radially placed with 120° intervals. This design aims

to avoid kinematics singularity, where no output torque can be

generated regardless of how the cylinders are actuated.

However, for fluid-driven cylinders that only allow for push

motion, singularity becomes inevitable if only one or two

cylinders are employed in a craft-shaft mechanism. This

necessitates a minimum of three-cylinder design to enable

smooth rotary motion. The allowable output torque could also

be increased by employing additional cylinders.

B. Kinematics model

Kinematics of the three-cylinder configuration is derived

based on the actuator geometry. Key kinematics parameters of

a single cylinder are depicted in Fig. 2d. All the components,

except for the rolling diaphragm, are considered as rigid bodies.

Unique solution of each piston displacement, ix , is obtainable,

corresponding to an angular position θ of the output shaft. By

applying Cosine Law for the triangle OAP∆ in Fig. 2c, the

piston displacement of the cylinder C1 can be calculated as:

( )( ) 2

1( ) c s2 o1x sR R s sθ θ−= + + − . (1)

As the pistons are evenly placed in a circle, the ith cylinder Ci

has a phase difference ( 1) 2 /i i nϕ π= − ⋅ compared with

cylinder C1 where n is the total number of cylinders and equals

to 3 for the three-cylinder configuration. Therefore, the piston

displacements of the cylinders can be derived by adding the

phase difference to θ in (1). Note that the misalignment is

negligible for the installation of the rotating plate.

C. Dynamics model

To identify the system properties and optimize the design

parameters, we established the model of the integrated

transmission system and carry out the validation, not only in

simulation but also in the experimentation. Provided with the

dynamics model of our proposed actuator, we can identify the

key parameters that govern the system performance, hence

defining a design guideline to fulfill various practical

requirements and constraints.

The proposed transmission system adopts a master-slave

design, with two sides connected by several hydrostatic

transmission pipelines. The slave side is the three-cylinder

actuation unit, while the master side comprises of the same

number of cylinders individually driven by electric motors. The

system dynamics model is derived in two sections, namely the

slave actuation unit and the hydraulic transmission.

1) Dynamics modeling of slave actuation unit

Two assumptions are taken into account: 1) all the

components are rigid body, except for the rolling diaphragm

and pipelines; 2) friction at the joints is negligible. Each

cylinder can only generate a unidirectional force, which comes

from the fluid pressure in the pipeline. The output torque

contributed by the ith cylinder can then be described as

i i iF dτ = ⋅ , where iF is the force provided by the cylinder and

id is the offset between the center line of the ith piston and the

rotation axis of output shaft. From Fig. 2c, id can be calculated

as sini id R β= ⋅ , where R is the rotational radius and iβ

denotes the angle between the axis of the ith piston rod and AO.

Here sin iβ can be calculated by Sine Law as:

( )

( )2 2

sinsin

2 cos

i

i

i

s

s R s R

θ ϕβ

θ ϕ

⋅ −=

+ − ⋅ −. (2)

The torques generated by the cylinders are summed and applied

at the crankshaft as:

1

n

i r o

i

Iτ τθ=

= + ɺɺ , (3)

where �� is the inertia of the rotational components, θɺɺ is the

angular acceleration of output shaft and oτ is the output torque.

Thus, the correlation between the output torque and the forces

provided by the cylinders can be described. Torque control is

then made possible to be implemented on this actuator. 2) Dynamics modeling of hydraulic transmission

This section details the dynamics model of the rolling

diaphragm-based hydraulic transmission, which describes the

Fig. 3. Dynamics parameters of a single-pipeline transmission. Input force ��is applied to move Piston 1 at constant velocity, with output force �� equal to zero. The cross markers “×” denote the fluid damping.




relation between the input force inF from the master side to the

output force of outF at the slave side. A spring-mass-damping

system (Fig. 3) is adopted to approximate the interactions

between the pistons and hydraulic fluid. Their interconnection

is represented by the spring elements of stiffness 2 tK , which

account for the pipeline compliance and fluid compressibility.

We assume that the system damping induced by the rolling

diaphragm and fluid friction can be described by the

coefficients c and fB .

We first derive the pipeline compliance by considering that

the input force inF is applied at Piston 1 while the Piston 2 is

blocked. The following equations in (4) describe the hoop

stress θσ and radial stress rσ at the inner pipe wall in

response to the applied pressure P, according to Lamé Formula:

2 2

2 2,

pi po

r

po pi

D DP P

D Dθσ σ

+= ⋅ = −

−, (4)

where poD and pi

D denote the outer and inner diameters of the

pipeline. For pipes made of isotropic material with modulus of

elasticity E and Poisson’s ratio υ , the hoop strain is equivalent

to / ( ) /pi pi r

D D Eθ θε σ υσ= ∆ = − . The volume change in the

pipe for an enclosed system should be equal to the change in the

input cylinder, which gives 2 2 2[( ) ]pi pi pi p in inD D D L D x+ ∆ − = ⋅ ∆ ,

where piD∆ is the change of pipe inner diameter, inD is the

diameter of input cylinder, inx∆ is the displacement of input

piston and pL is the length of pipe. Therefore, the inner

diameter change of pipe could be determined by:

2 /(2 )

pi in in pi pD D x D L∆ ≈ ⋅∆ . (5)

With (4) to (5) and the assumption that the pressure comes

from the input force 2( / 4)in in

F P Dπ= ⋅ , the pipeline stiffness

pK observed at the piston can be derived as:

12 2 2 24

2 2 28

pi po po piin in

p

in pi p po pi

D D D DF EDK

x D L D D

υ υπ−

+ + −= =

∆ − . (6)

The fluid stiffness due to compression could be modeled as 2 /

f v inK E A V= ⋅ , where inA is the cross-sectional area of the

input cylinder, V is the total volume of fluid and vE is the fluid

bulk modulus. Hence, the equivalent transmission stiffness tK

of the hydraulic pipe can be calculated as the series of pipeline

compliance and fluid stiffness: / ( )t p f p f

K K K K K= + .

For the system damping factors, we assume that the input

force at Piston 1 is inF and it produces a movement at constant

velocity, given that there is zero loading at the Piston 2 (

0outF = ). We can hence derive the fluid head loss, which is

governed by the Bernoulli equation for steady and

incompressible flow between any two points in a pipe:

2 2

2 2in in out out

in out f

P v P vgz gz h

ρ ρ+ + = + + + , (7)

where inP and outP represent the fluid pressures, inv and outv

are the fluid velocities, inz and outz represent the elevations, at

the input and output piston respectively, fh is the head loss ρ

is the fluid density and g is the gravitational constant.

In this case, pipeline loss mainly contributes to head loss,

while the local loss at the connections between cylinder and

tube can be neglected. Because the pipeline loss is proportional

to the length but inversely proportional to the diameters, the

head loss in the cylinders is negligible when compared with that

in the pipelines. The total pipeline loss can be approximated as 2 / (2 )

f p f pih L v Dλ= , where λ is the flow coefficient and f

v

is the fluid velocity [22]. For laminar pipe flow, we can assume

that 64 / eRλ = , where the Reynolds number /e f pi

R v Dρ µ= ,

and µ is the dynamic viscosity of fluid.

Assuming that the pipes are put at the same elevation, the

terms ingz and out

gz can be eliminated. The fluid is nearly

incompressible so that the velocity at the input and output

piston is approximately equal. The pressure outP is zero in our

case with no load ( 0out

F = ). By observing that in in inF P A= ⋅ ,

the equivalent damping coefficient fB can be obtained as:

4

8in in

f P

in pi

F DB L

v Dπµ

= =

. (8)

For the fluid inertia, we consider an equivalent fluid mass as

observed at the piston, which can be determined by an energy

calculation 2 2 2 ,

f in cyl in pi fm v m v m v= + where fm is the

equivalent mass of fluid, cylm is the fluid mass in cylinder, and

pim is the fluid mass in the pipeline. Then the equivalent mass

can be obtained as 4( / )

f cyl pi in pim m m D D= + .

The key components of the overall dynamics model of the

passive fluid transmission system are shown in Fig. 3. The

dynamics of the hydraulic transmission can be described by a

linear differential equation as follows:

+ + =Kq Cq Mq Fɺ ɺɺ , (9)

where

( )

[ ]

2 2 0

2 4 2 , ,

0 2 2

( , , ) 0

t t

t t t f

t t

T

p f p in out

K K

K K K diag c B c

K K

diag m m m F F

−

= − − = − = = −

K C

M F

. (10)

In (9), 1 2 3[ ]Tq q q=q denotes the matrix containing

displacements of input piston ( 1q ), fluid ( 2q ) and output piston

( 3q ). Damping coefficient, c, is introduced by the rolling

diaphragm. The state space function can be derived as:

-1 -1 -1

0 0 = + − −

q I q

q M K M C q M F

ɺ

ɺɺ ɺ. (11)

D. Design considerations

This section presents the design guidelines for the hydraulic

system in regards to the desired system performance, namely

fluid transmission stiffness and latency. Parametric study is

performed by numerical simulation of the dynamics model. The

study scope includes many form factors of the transmission




system, such as pipe diameter, length, thickness, materials, and

cylinder diameter. Four typical pipe materials:

polycaprolactam 6 (PA 6), PA 66, polytetrafluoroethylene

(PTFE) and polyurethane (PU), are examined.

Transmission stiffness – The transmission stiffness has a

compelling effect on the system repeatability and accuracy.

Fig. 4a-b illustrate the trends of transmission stiffness under

various pipe diameters and lengths. The stiffness decreases

when the diameter or the length increases. It can also be

observed that the choice of pipe material imposes a significant

influence on the transmission stiffness. PA66 offers the highest

transmission stiffness because it possesses the highest Young’s

modulus. However, the large bending stiffness of PA66 (0.17

N-m2 with outer/inner diameter of Ø6/4 mm) hinder its

application in conditions that requires flexible arrangement.

Fig. 4c shows that the enlargement of piston diameter could

also enhance the transmission stiffness, due to the increased

piston diameter to pipe inner diameter ratio.

Transmission latency – The power transmission in this

system could be considered as the simultaneous occurrence of

pressure and velocity changes. Such velocity of pressure

transient through fluid in a closed conduit could be deduced as:

1

pi

p

p v

Dc

T E E

ρψ ρ−

= + ⋅

, (12)

where the parameters are summarized in Table I [23]. The pipe

support factor ψ is a function of the pipe material (υ ), the

pipe inner diameter ( piD ) and the pipe wall thickness ( p

T ),

which can be calculated as following for the case of

thick-walled pipe ( / 10pi p

D T < ) without anchorage throughout

the length [23]: 2 (1 ) / / ( )pi pi pi pe D D D Tψ υ= + + + .

Fig. 4d shows that the latency with baseline parameter

values is around 21 ms (with the ratio of pipe inner diameter to

thickness varying and pipe thickness fixed at 1 mm). The

enlargement of pipe inner diameter over 2 mm causes a slight

increase of the latency. But the decline of the diameter under 1

mm will bring the significant rise in latency. Meanwhile, the

latency is also proportional to the pipe length. And more rigid

pipe material will reduce the transmission latency.

Overall, several design tradeoffs are developed to account

for the required dynamics performance and dedicated operating

conditions. Shorter pipelines are preferable as a general design

rule to reduce the fluid inertia, give rise to a higher transmission

stiffness, and decrease the transmission latency. For surgical

applications that emphasize positional accuracy, such as breast

or prostate biopsy, pipelines with a smaller diameter and

pistons with a larger diameter should be adopted to enhance the

transmission stiffness. However, a small pipe diameter (< 2mm)

will dramatically increase transmission latency and damping,

which will deteriorate the control and stability. Therefore, the

pipeline diameter shall be expanded to accommodate for

applications that require a rapid dynamic response, such as

tele-manipulation of a catheter in a master-slave manner.

III. EXPERIMENTAL RESULTS

We have conducted several experiments to evaluate key

performance indices of the proposed hydraulic transmission,

including step response, force dynamic transmission, positional

frequency response and sinusoidal positional tracking. In all

these experiments, master and slave components of the

transmission were connected by 10-meter semi-rigid nylon (PA

6) tubes, which had inner and outer diameters of ID:Ø4 mm and

OD:Ø6 mm, respectively. We choose distilled water as the

hydraulic fluid, accrediting to its availability and ease of

implementation. The water pressure pre-loading in all pipelines

was controlled by a pressurized air supply system, a pressure

regulating valve and a fluid reservoir. Not only could this

eliminate backlash, but it could also ensure the symmetric

folding/unfolding of rolling diaphragms, thus reducing friction

during fast motion transmission.

A. Step response of the single-cylinder actuation

Step response experiments were conducted to evaluate the

force transmission behavior in a pipeline with both ends of

cylinders (Fig. 2). At the master side, a DC motor

(HFmotor-40150, Chengdu Hangfa Hydraulic Engineering Co.,

Ltd) actuated the master cylinder through the rack-and-pinion

mechanism, which transmitted torque to linear force. The

output force at slave cylinder was measured by a force sensor

(MIK-LCS1, Hangzhou Meacon Automation Technology Co.,

Ltd) embedded on the piston rod. Water in the pipelines was

preloaded at 0.05 MPa to ensure the mechanical couplings were

fully engaged, which corresponded to 5 N force output on the

slave cylinder at the initial state. Two step inputs, i.e. 26 N and

78 N, were applied to the master cylinder. The corresponding

measured force responses are shown in Fig. 5. Simulated

results deduced by the dynamics model in Section II.D are also

overlaid, predicting a similar response to the measured results.

The response time is within 40 ms from the signal input and the

TABLE I PHYSICAL PARAMETERS

Parameter Description Parameter Description

pc Velocity of pressure transient in fluid

υ Poisson’s ratio of pipe material

vE Bulk modulus of fluid piD Pipe inner diameter

E Young’s modulus of pipe material

Pipe wall thickness

ρ Fluid density ψ Pipe support factor

Fig. 4. Simulation showing the trend of transmission stiffness against: (a) pipe inner diameter; (b) pipe length; and (c) piston diameter. It can be observed that the stiffness profile is significantly affected by the pipe materials: PA 6, PA66, PTFE and PU.




10%-to-90% rise time is 25 ms for both step input forces. This

rise time remains constant for different input forces, depicting

an important feature for a linear time-invariant system. The

settling time with 5% error band is about 0.17 s, indicating that

the proposed hydraulic transmission can rapidly transmit the

force, even via a 10-meter long pipeline. These characteristics

are crucial to the highly responsive force transmission required

in many typical teleoperated robot systems.

B. Force transmission performance

Force transmission performance of the three-cylinder

continuous motor (Fig. 1) was evaluated in a weight-lifting

experiment, in which three master cylinders were individually

actuated by electric motors through leadscrew drives. The

output shaft was coupled to a winch of diameter Ø40 mm. With

the hydraulic fluid pre-loaded at 0.1 MPa, the master-slave

actuator can lift 2.5 kg at a constant velocity of 50.24 mm/s,

corresponding to an output torque of 0.49 N·m and a net power

of 1.23 W. The volumetric power density of the hydraulic

transmission is 2.46 kW/m3. The torque/power outputs of this

motor are mainly determined by the electric motor inputs at the

master side. In principle, the continuous motor can generate

power as much as the electric motors can afford, until the

weakest component with lower strength limit fails, e.g. tiny

gear teeth and thin rolling diaphragms.

C. Positional frequency response

The dynamic performance of a three-cylinder continuous

actuator (Fig. 1) was investigated with a frequency response

method. No loading was added to the slave actuator. The three

master cylinders were controlled based on the inverse

kinematics derived in Section II.C. The slave actuator could

thus follow the periodic sinusoidal input of master actuator

under open-loop control, where the angular position �

� sin�� ⋅ ��. The amplitude was 5° and the test frequency was

from 0.1 Hz to 7 Hz. The output angular position was measured

by a differential encoder coupled with the output shaft.

Fig. 6 illustrates the Bode plots of magnitude � and the

phase-shift � of the continuous actuator at steady state. Note

that for a linear time-invariant system, the frequency response

at steady state becomes �� ⋅ � sin�� ⋅ � � �� . The

magnitude plot indicates that the magnification increases with

the preloaded fluid pressure. The magnification value peaks at

around 5 Hz, which corresponds to the natural frequency of the

overall hydraulic transmission. The phase lag of the

transmission is kept at around 20.3° for low actuation

frequency (≤ 2 Hz). It is also found that the increase of the

preloaded fluid pressure does not significantly affect the natural

frequency and phase lag. The transmission with preloaded fluid

pressure 0.2 MPa had small time delay: only 60 ms and 52 ms at

actuation frequency 1 Hz and 5 Hz, respectively.

D. Sinusoidal positional tracking

To evaluate the accuracy of the 3-cylinder actuator under

open-loop control, a positional tracking test was performed.

The setup was the same as described in Section III.C, but the

periodic sinusoidal input at the master side is less frequent,

once per 20 s (0.05 Hz), covering a larger motion range of 360°.

This sinusoidal tracking performance is illustrated in Fig. 7,

which shows the input and output angular motion profile

overlaid, as well as the corresponding error in angular

displacement. It also demonstrates that the 3-cylinder

continuous actuator can track the positional input over the

range of 360°. The average error between the input and output

within one cycle is 0.64°, ensuring the proposed actuator can be

Fig. 7. Sinusoidal tracking of angular displacement during the three-cylinder actuation throughout two cycles in 40 s. Precise feed-forward control is observed, with an average absolute error of 0.64°.

Fig. 6. Experimental frequency response of the three-cylinder actuation at four levels of hydraulic pressure. The input is positional signal of electric motor (master), and the output is the encoded position of our motor (slave).

Fig. 5. Step response of a single cylinder transmission, which were measured in two different steps of magnitudes. Experimental and modeled responses are compared. The response time from the signal input is within 40 ms.




manipulated by open-loop control accurately.

In summary, the master-slave actuator has fast step response

(< 40 ms), high payload (0.49 N·m), quick frequency response

(60 ms at 1 Hz and 0.2 MPa), and precise feed-forward control

(ave. error of 0.64°). The performance in step response (Fig. 5)

and frequency response (Bode plot, Fig. 6) have demonstrated

the sufficiently low latency of force/position transfer within the

range of 0.1-2 Hz. Compared with the previous two-cylinder

actuator presented in [19], the key improvement of the new

three-cylinder hydraulic motor is to provide continuous

bidirectional actuation with unlimited motion range. In

addition, it can achieve a significant improvement in accuracy

to 0.64°/1.50° (avg./max.), while the accuracy of previous

actuator is 1.46°/2.56° (avg./max.). It can be attributed to our

the reduced friction in the new three-cylinder crank shaft

design, without using any plastic gear. The frequency response

remains similar due to the unchanged hydraulic pipeline

parameters (e.g. diameter, length, material, transmission fluid).

IV. MR SAFE ROBOT FOR CARDIAC CATHETERIZATION

The proposed three-cylinder hydraulic motor is incorporated

into an MRI-guided robotic catheter platform [19, 24] (Fig. 8a).

This aims to improve the catheter insertion/reciprocating

motion. Not only does it enable long range catheter

advancement (340 mm) in the human body, but it also allows

rapid push/pull of catheter with high fidelity. This feature is

crucial for delicate EP tasks, such as electro-anatomic mapping

(EAM) and radiofrequency (RF) ablation for cardiac EP. The

steering and rotation of catheter are achieved by our previous

two-cylinder actuators with a motion range of ±45° and ±360°

respectively. An EP catheter (Thermocool Bi-Directional

Catheter, Biosense Webster Inc.) can be readily integrated to

the robot, providing full range tip steering of ±180°.

To evaluate this tele-operated robotic catheterization, an

experiment was conducted to simulate the long-range

navigations, such as from femoral vein to heart chamber.

Eleven rings (ID=Ø7 mm) were placed serially along 310-mm

distance with an average spacing of 31 mm (Fig. 8b). The

detailed dimensions are stated in Fig. 9a. A smooth curve

linking the ring centers in series simulates a path along the

vessel to heart chamber (Fig. 9b). This task would be found

more difficult relative to the navigation in human vein

(ID≈Ø9.4 mm) and inferior vena cava (ID≈Ø20 mm) [25, 26].

During the task, a standard EP catheter with an outer

diameter of 8 Fr (≈Ø2.7 mm) is manipulated by the robot that is

tele-controlled by a 3D motion input device (Novint Falcon,

NF1-L01-004). To record the position and orientation (pose) of

the catheter, a 6-DoF EM positional sensor (Ø0.8×9 mm, NDI

Fig. 9. (a) Key parameters of the experimental setup and the catheterization performance indices; (b) Actual footprint of the catheter tip compared with the reference curve along the series of rings of 1st–6th (Upper) and 7th–11th (Lower). The more the catheter tip deviated from the reference curve, warmer the color of its tip footprint. A large difference in the orientation of two adjunctive rings, e.g. from the 8th to the 9th, makes the navigation challenging.

Fig. 8. MR safe robot prototype incorporating 3 sets of hydraulic transmission units for 3-DoF manipulation of a standard EP catheter. A three-cylinder unit pushes/pulls the catheter precisely in long-range navigation. Master-slave motion is transmitted from control to MRI room through a pair of 10-meter long pipelines. (b) EP ablation catheter tele-manipulated to pass through a series of 11 rings. The 3-D position of catheter tip is EM-tracked for our validation; (c) Block diagram illustrating the architecture of the robotic catheter system.




Medical Aurora), with a tracking accuracy of 0.48mm, is

attached near the catheter tip (Fig. 8b). A subject, who learned

the robot control in advance, was invited to perform the task.

The subject could look at the catheter tip, and adjust the

manipulation so as to pass through the rings. Fig. 8c illustrates

the system architecture of the robotic catheter system.

The diagrams in Fig. 9b depict the catheter tip footprint

along the series of 11 rings. The deviation from the tip to the

reference curve is indicated by the warm color gradient. A

mean value of deviation, 3.03 mm, was found throughout the

entire trajectory. Most sections of navigation are smooth and

closed along with the reference curve. But several sections of

the tip footprint involve more deviations, particular when the

orientation difference of adjacent rings is relatively large.

V. CONCLUSION

We present a design of an MR safe hydraulic motor that

incorporates three rolling-diaphragm-sealed cylinders.

Mechanical power can be transferred through the passive

hydrostatic transmission along the long hydraulic tubes. Unlike

the two-cylinder motor design, the presented motor can provide

continuous bidirectional rotation with unlimited range. It also

features fast response (rise time < 40 ms), precise open-loop

control of position (averag error of 0.64°) and high output

torque (0.49 N·m) through 10-meter long hydraulic pipelines.

Currently, there is no such kind of MR safe hydraulic

master-slave follower. Both kinematics and dynamics models

of the motor have also been devised to identify the key design

parameters that govern the system performance, namely

transmission stiffness and latency. Their design tradeoff is also

presented in an analytical study.

To further evaluate the practical value of our motor, we have

integrated it into an MRI-guided catheter robot for cardiac EP.

This shows its capacity to perform high-fidelity

tele-manipulation of the standard EP catheter, and also its

potential in other types of interventions demanding for intra-op

MRI guidance, such as breast, prostate biopsy, stereotactic

neurosurgery [27]. This robot-assisted approach would add

much confidence to surgeons with sufficient MR-based

guidance revealed on multiple displays in the control room.

We also foresee that MRI-guided HIFU thermal therapy is

another emerging intervention that could benefit from the

present motor. The high-payload, continuous actuation would

facilitate accurate repositioning of the large array of ultrasound

transducers, hence enlarging the ablation workspace, and also

smoothening the interventional workflow without having to

going in-and-out the MRI room for manual repositioning.

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